Statistical distribution and spectral analysis of rainfallanomalies for Barcelona (NE Spain)

Summary  Rainfall anomaly patterns are obtained for the city of Barcelona from a statistical and a spectral point of view. The time series consists of monthly rainfall amounts recorded over 128 years without interruption. Monthly positive and negative anomalies, obtained as the difference between monthly amounts and monthly threshold values, are used for both types of analyses. The threshold levels are derived form the deciles of theoretical monthly rainfall distributions, which have been previously modelled by the gamma distribution. Positive and negative anomalies of the monthly rain amounts are investigated for these threshold levels. The statistical analysis is applied to each decile considered, yielding empirical exponential laws that can be used to forecast the cumulative number of episodes of consecutive months with either positive or negative anomalies equalling or exceeding a fixed length. A set of linear laws, relating the expected rainfall amount cumulated during an episode of a fixed length, is also deduced. It is worthy of mention that, independently of the decile considered, all the exponential and linear laws have satisfactory regression coefficients. At the same time, it has also been possible to establish the evolution of the coefficients of these laws with respect to the different deciles considered. The exponential laws for episodes of positive and negative anomalies are the starting point, together with two hypotheses, to model probabilities of repeated long episodes over an arbitrary number of years and their return periods in terms of the Poisson distribution model. Moreover, power spectra are derived for anomalies relative to the 50% decile at monthly and seasonal scale. The spectral estimates obtained are then compared with theoretical spectra deduced from possible Markovian or random behaviour of the time series of anomalies. Finally, the significant spectral peaks are discussed and compared with other significant spectral components deduced for some areas of the Mediterranean domain. Received November 11, 1999 Revised February 28, 2000     

Rapid transitions and ultra-low frequency behaviour in a 40 kyr integration with a coupled climate model of intermediate complexity

 A 40 kyr integration with the coupled atmosphere/ocean/sea-ice model of intermediate complexity ECBilt for present boundary conditions has been performed. The climate of ECBilt displays quasi-periodical behaviour with a period of approximately 13 kyr. The quasi-periodical behaviour is characterized by large changes in the overturning cell in the Southern Ocean. The southern cell fluctuates between two quasi-stationary states, with accompaning changes in the atmospheric circulation in the Southern Hemisphere. The transition between these states is rapid and resembles the polar halocline catastrophes and flushes as observed in ocean general circulation models under mixed boundary conditions. The sea-ice influence on both the surface heat and fresh water flux appears to be crucial for the existence and the prolongation of the quasi-stationary states. The atmospheric circulation of those two quasi-stationary states displays large regional differences over Antarctica, resulting in even opposite surface air temperature trends for certain locations during the transition from one state to another. Received: 7 October 1999 / Accepted: 28 August 2000     

An Analytical Footprint Model For Non-Neutral Stratification

We propose an analytical model for the so-called footprint of scalar fluxes in the atmospheric boundary layer. It is the generalization of formulations already given in the literature, which allows to account for thermal stability. Our model is only marginally more complicated than these, and it is therefore simple enough to be applicable for a routine footprint analysis within long-term measurements. The mathematical framework of our model is a stationary gradient diffusion formulation with height-independent crosswind dispersion. It uses the solution of the resulting two-dimensional advection – diffusion equation for power law profiles of the mean wind velocity and the eddy diffusivity. To find the adjoint Monin–Obukhov similarity profile, we propose two different approaches, a purely analytical one and a simplenumerical error minimalization.     

Localized multi-scale energy and vorticity analysis: II. Finite-amplitude instability theory and validation

A novel localized finite-amplitude hydrodynamic stability analysis is established in a unified treatment for the study of real oceanic and atmospheric processes, which are in general highly nonlinear, and intermittent in space and time. We first re-state the classical definition using the multi-scale energy and vorticity analysis (MS-EVA) developed in Liang and Robinson [Liang, X.S., Robinson, A.R., 2005. Localized multiscale energy and vorticity analysis. I. Fundamentals. Dyn. Atmos. Oceans 38, 195–230], and then manipulate certain global operators to achieve the temporal and spatial localization. The key of the spatial localization is transfer-transport separation, which is made precise with the concept of perfect transfer, while relaxation of marginalization leads to the localization of time. In doing so the information of transfer lost in the averages is retrieved and an easy-to-use instability metric is obtained. The resulting metric is field-like (Eulerian), conceptually generalizing the classical formalism, a bulk notion over the whole system. In this framework, an instability has a structure, which is of particular use for open flow processes. We check the structure of baroclinic instability with the benchmark Eady model solution, and the Iceland–Faeroe Frontal (IFF) intrusion, a highly localized and nonlinear process occurring frequently in the region between Iceland and Faeroe Islands. A clear isolated baroclinic instability is identified around the intrusion, which is further found to be characterized by the transition from a spatially growing mode to a temporally growing mode. We also check the consistency of the MS-EVA dynamics with the barotropic Kuo model. An observation is that a local perturbation burst does not necessarily imply an instability: the perturbation energy could be transported from other processes occurring elsewhere. We find that our analysis yields a Kuo theorem-consistent mean–eddy interaction, which is not seen in a conventional Reynolds stress framework. Using the techniques of marginalization and localization, this work sets up an example for the generalization of certain geophysical fluid dynamics theories for more generic purposes.     

An Approach to Quantify the Heat Wave Strength and Price a Heat Derivative for Risk Hedging

Mitigating the heat stress via a derivative policy is a vital financial option for agricultural producers and other business sectors to strategically adapt to the climate change scenario. This study has provided an approach to identifying heat stress events and pricing the heat stress weather derivative due to persistent days of high surface air temperature (SAT). Cooling degree days (CDD) are used as the weather index for trade. In this study, a call-option model was used as an example for calculating the price of the index. Two heat stress indices were developed to describe the severity and physical impact of heat waves. The daily Global Historical Climatology Network (GHCN-D) SAT data from 1901 to 2007 from the southern California, USA, were used. A major California heat wave that occurred 20-25 October 1965 was studied. The derivative price was calculated based on the call-option model for both long-term station data and the interpolated grid point data at a regular 0.1 ×0.1 latitude-longitude grid. The resulting comparison indicates that (a) the interpolated data can be used as reliable proxy to price the CDD and (b) a normal distribution model cannot always be used to reliably calculate the CDD price. In conclusion, the data, models, and procedures described in this study have potential application in hedging agricultural and other risks.     

Role of the Tibetan Plateau thermal forcing in the summer climate patterns over subtropical Asia

The mechanism of the Tibetan Plateau (TP) thermal forcing in influencing the summer climate patterns over subtropical Asia is investigated by means of NCEP/NCAR reanalysis diagnosis. Results show that since the TP is a huge elevated heating source with the strongest heating in the surface layers in summer, the thermal adaptation results in a shallow cyclonic circulation near the surface and a deep anticyclonic circulation above it. According to the steady barotropic vorticity equation for large scales, airflow must converge in the lower layers and diverge in the higher layers over the eastern side of the TP. However, the western side of the TP is characterized by a reversed structure, i.e., divergence in lower layers but convergence in higher layers. Hence, pumping and sucking processes bring in upward and downward movement over the east and west sides of the TP, respectively. Such a circulation is embedded in the large-scale circulation that is forced by the Eurasian continental heating. Because the TP together with Iran Plateau are located at the central and eastern parts of the continent, and, because the orography-induced circulation is in phase with the continental scale circulation, the role of the TP thermal forcing is to intensify the East Asian monsoon to its east and the dry and hot desert climate in mid-Asia to its west. The summertime thermal forcing of the Rockies and Andes can generate similar circulations along the two subtopics as the TP does since they are located near the western coasts. But, the lower troposphere poleward flow that is induced by orographic thermal forcing does not coincide with the poleward flows over the eastern coastal region that is induced by continental heating and the monsoon rainfall in North and South America is not as strong as in East Asia. However, the equatorward flow and the associated subsidence induced by the two mountain ranges along the western coasts of both North and South America are in phase with those induced by continental heating. These contribute to the formation of the stable low stratus clouds and strong long-wave radiative cooling over the eastern subtropical Pacific regions just off the western coast of the continent.     

The second order adjoint analysis: Theory and applications

Summary The adjoint method application in variational data assimilation provides a way of obtaining the exact gradient of the cost functionj with respect to the control variables. Additional information may be obtained by using second order information. This paper presents a second order adjoint model (SOA) for a shallow-water equation model on a limited-area domain. One integration of such a model yields a value of the Hessian (the matrix of second partial derivatives, ² J) multiplied by a vector or a column of the Hessian of the cost function with respect to the initial conditions. The SOA model was then used to conduct a sensitivity analysis of the cost function with respect to distributed observations and to study the evolution of the condition number (the ratio of the largest to smallest eigenvalues) of the Hessian during the course of the minimization. The condition number is strongly related to the convergence rate of the minimization. It is proved that the Hessian is positive definite during the process of the minimization, which in turn proves the uniqueness of the optimal solution for the test problem. Numerical results show that the sensitivity of the response increases with time and that the sensitivity to the geopotential field is larger by an order of magnitude than that to theu andv components of the velocity field. Experiments using data from an ECMWF analysis of the First Global Geophysical Experiment (FGGE) show that the cost functionJ is more sensitive to observations at points where meteorologically intensive events occur. Using the second order adjoint shows that most changes in the value of the condition number of the Hessian occur during the first few iterations of the minimization and are strongly correlated to major large-scale changes in the reconstructed initial conditions fields.With 17 Figures     

Characteristics and simulation of lightning current waveforms during one artificially triggered lightning

In the summer of 2005, one negative lightning flash was artificially triggered in Shandong Province (117°48′ E, 37°42′N), middle latitude region of eastern China. The flash included 10 return strokes, and the geometric mean value of the current peak was 11.9 kA (the average value was 12.6 kA) with a maximum of 21.0 kA and a minimum of 6.6 kA, similar to the subsequent return strokes in natural lightning. The geometric mean value of half peak width was 39 μs (the average value was 40 μs), which was much larger than the usual result. Based on the Diendorfer and Uman (DU) model, the return-stroke current waveforms and charge distribution along the lightning channel are discussed. The simulated current waveforms, being divided into breakdown and corona current components, are in agreement with the optical measurements when the two different discharge time constants are properly chosen.     

Biases in AMIP model simulations of the east China monsoon system

 AMIP model simulations of the east China (5–50°N; 105–122°E) monsoon system are analyzed to study coherent relationships between rainfall and wind annual cycle biases. A comparison with observed interannual variability patterns is carried out to identify the physical processes that explain the biases. The analyses show that poleward displacement of the simulated east Asian jet stream causes the ascending branch of the jet-induced transverse circulation to move north and, as a consequence, produces negative (positive) rainfall biases occur in central (northeast) China. The model simulations show decreased southwesterly flow and ITCZ rainfall over the South China Sea when weaker (versus observations) summer Hadley and Walker circulations are present. This results from diminished model tropical disturbance activity, and highlights the importance of air-sea interactions. In addition, during October–January, intensified model low-level easterlies enhance moisture transport and produce positive local rainfall biases over central and northeast China. Biases in the east China monsoon system are concurrently reflected in the planetary circulation. Enhanced northeast China rainfall results from increased surface pressure over the North Pacific and an amplified zonal pressure gradient along the east China coast. This bias pattern is associated with differences in model representations of topography. On the other hand, the South China Sea experiences an extensive elongated meridional rainfall bias dipole structure that straddles the equator. This is accompanied by a baroclinic vertical pattern over the tropics as well as a barotropic wave train that extends from Australia to the Antarctic, where the teleconnection is likely a direct atmospheric response to tropical convective heating. Received: 20 June 2000 / Accepted: 17 September 2000